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Gold melts at almost 2000°F (1945°F to be exact; 1063°C) and can be done at home by using a propane torch ($40 at home improvement stores). The propane torch will take a while to get the gold to be hot, then soft, and finally completely melt. Using an oxy-acetelyne torch will speed up the process, but I don't consider that a standard household tool. However, I don't recommend you try this unless you are experienced with this sort of activity.

There have also been some experiments involving conventional (unmodified) microwave ovens and the melting of metals.

You could likely do it with a MAPP or a turbo torch, but for anything but a bit of wire you would want a small baffle furnace -- you could make an ersatz one one with a few fire bricks (preferably the soft kind), to contain the heat. Or you could use such a furnace with charcoal and forced air. You are essentially making your own equipment such as a jeweler -- or a goldsmith in a primitive culture -- would use.

Keep in mind that you would probably not be trying to melt pure gold, but an alloy which would require a lower temperature than 24K.